In the xy-plane, the lines with equations 2x+2y=1 and 4x−y=4 intersect at the point with coordinates (a, b). what is the value of b ?

I recommend solving the second equation above for y.  That will be y=4x-4.  Now sub that value of y into the first equation for y and get 2x+2(4x-4)=1.  Expand to get 2x + 8x - 8 = 1.  Combine like terms and we get 10x = 9 and .  Now we need to plug that x value into any equation we have to solve for y (your "b").  and .  Then .  Multiplying both sides by 1/2 gives us that y = -2/5.  That's your "b" value you're looking for.